A Completely Inadequate Bibliography of the History of
Mathematics

Caveat: This is neither exhaustive nor unbiased.
Primarily, it consists of books that I have read that I will vouch
have some value (even if the value is entertainment, as in Bell's
book). Most of the following books are aimed at the professional
non-mathematician (i.e., someone to whom the land of mathematics is an
interesting place to visit, but you wouldn't want to live there).

A note about the ratings: Again, no claim of objectivity is
made. However, the following rating system is fairly objective, as it
indicates the amount of mathematical background necessary to truly
understand the information contained:

+

Comprehensible with even the most basic mathematics
background.

!

Some mathematics, but nothing too extreme; if you
can recognize the "!" symbol, you should be OK.

!!

A bit more difficult, though a year's worth of
calculus or so should give you enough background to appreciate it; you
can "blip" over the scarier mathematics.

!!!

Tough stuff. Best suited for math majors, or
people who are really interested in the subject.

General

If I had to pick one...: Kline's is probably the best single
volume history of mathematics that I know of for those who want to
truly understand the subject. While he is slightly guilty of
modernizing the notation, he is faithful to the original source
material as well, and his extensive bibliography is a good jumping off
point for further reserach.

A history of mathematics, Carl Boyer. Rating: +

Excellent introduction to the history of mathematics, especially
for a non-mathematician. Unlike many other introductions, Boyer does
not spend all his time on the Greeks and Renaissance Italians, but
tries to cover the entire history of mathematics from ancient Egypt to
the 20th century.

Very good introduction to the history of mathematics, though Kline
does spend most of his time in analysis (calculus and its spinoffs).
Every chapter contains an excellent bibliography.

Number Words and Number Symbols, Karl Menninger.
Rating:+

A fascinating introduction to numbers and how different cultures
represent them and compute with them. A bonus: Menninger includes the
quotes both original and translated quotes.

Arithmetic

Capitalism and arithmetic, Frank Swetz.

Includes Smith's translation of The Treviso Arithmetic, the
first printed mathematics text. A fascinating portrait of mathematics
at the beginning of the 16th century.

Algebra

A history of algebra, from al-Khwarizmi to Emmy Noether,
B. L. van der Waerden. Rating: !

A good account of its subject matter. However, van der Waerden
takes great liberties in "modernizing" the notation used by
the older authors, which makes for easier reading by a modern
audience, though it loses some of the historical flavor (as much of
the development of mathematics is the development of mathematical
notation).

Geometry

If I had to pick one...It would be Heath's Euclid,
hands down.

The Elements of Euclid, Thomas L. Heath. Rating: +

If I was a medieval scholar, I would call this Heath's commentary
on Euclid, for that is what it is: it is Euclid's Elements, translated
and extensively footnoted. Heath traces many of the connections
between Euclid's work and the works of later mathematicians.

Calculus

The history of the calculus and its conceptual development,
Carl Boyer. Rating: !

Boyer spends a great deal of time discussing the earlier
development of calculus, up to Newton and Leibniz, and only the very
last section dealing with developments since then. However, you might
want to read:

The higher calculus: a history of real and complex analysis
from Euler to Weierstrass, Umberto Bottazzini. Rating: !!

A continuation of the study of the development of analysis. Its
!!! rating is mainly due to the fact that its subject matter is
usually reserved for graduate students; the book itself is very good
(speaking from my totally objective viewpoint of being one of
Dr. Hawkins' graduate students...) However, anyone with an !!
background can certainly appreciate the problem whose history Hawkins
addresses.

Analysis

Note: to make the historiography a bit more clear, I'm going to
differentiate this section from the section on calculus. (And if you
expect me to apologize for that awful pun, you little know me...

Zermelo's Axiom of Choice, Gregory H. Moore. Rating:
!!

The axiom of choice and its ramifications are discussed, as well
as the various paradoxes to arise out of it (such as Banach-Tarski and other
pathologies). While the mathematics itself is not too difficult, some
of the concepts might be a bit hard to take for the uninitiated, so it
gets the !! rating.

Number Theory

Number Theory and Its History, Oystein Ore. Rating:
!

This is more of a book on number theory than its history, though
it incorporates elements of both. Interesting for the one who wants
to know a little about the historical background to the solutions to
certain problems in number theory.

Applications of mathematics

In my totally unbiased opinion, this is something no home should
be without. Its length alone makes it valuable as a paperweight.

Sources of Mathematics

The World of Mathematics, James R. Newman. Rating: +

Excerpts from the writings of mathematicians, historians of
mathematics, and philosophers of mathematics, from ancient Egypt to
the modern age. (Overall the rating is +, though sometimes it
becomes !.)

A sourcebook in mathematics, David Eugene Smith.

A compilation of mathematical writings. Smith's selections are
mainly modern (only about a dozen date to before 1600), and not always
representative. A better sourcebook is:

A source book in mathematics, 1200-1800, D. J. Struik.

Just what it says; Struik's selections are much more
representative of mathematical development than Smith's.

Biographies of Mathematicians

Cardano: The Gambling Scholar, Oystein Ore. Rating:
+

A readable biography of Cardano; includes a sizable
discussion on the algebra of the 16th century.

Men of mathematics, Eric Temple Bell.
Rating: +

Contains biographies of a few dozen of the "great
mathematicians" of history. Warning: Bell's history is
suspect (and, in the case of Galois, almost entirely fictional), and
this work suffers especially from a lack of referencing. The best use
of this book is to point out interesting things for future study.

Georg Cantor, Joseph Warren Dauben. Rating: !

The history of the infinities developed by Cantor, and a biography
of Cantor as well.

The Mathematics of Sonya Kovalevskaya, Roger Cooke.
Rating: !

Sonya Kovalevskaya was one of the few women mathematicians of the
19th century, and as such would be a heroine to many groups regardless
of her abilities as a mathematician. However, Cooke examines her
mathematics as well, showing that she was also a first-class
mathematician.